login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A191822 Number of solutions to the Diophantine equation x1 x2 + x2 x3 + x3 x4 + x4 x5 = n, with all xi >= 1. 2
0, 0, 0, 1, 2, 6, 8, 16, 20, 32, 36, 58, 58, 86, 92, 125, 122, 178, 164, 228, 224, 286, 268, 382, 330, 436, 424, 534, 474, 660, 556, 740, 692, 840, 752, 1043, 846, 1094, 1032, 1276, 1078, 1476, 1204, 1582, 1458, 1710, 1480, 2070, 1628, 2096, 1924, 2332, 1946, 2652, 2148, 2770, 2480, 2908, 2480, 3512 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Related to "Louisville's Last Theorem".

REFERENCES

Andrews, George E., Stacked lattice boxes, Ann. Comb. 3 (1999), 115-130. See L_4(n).

E. T. Bell, The form wx+xy+yz+zu, Bull. Amer. Math. Soc., 42 (1936), 377-380.

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

G.f. = x^4 + 2 x^5 + 6 x^6 + 8 x^7 + 16 x^8 + 20 x^9 + 32 x^10 + ...

MAPLE

with(numtheory);

D00:=n->add(tau(j)*tau(n-j), j=1..n-1);

L4:=n->sigma[2](n)-n*sigma[0](n)-D00(n);

[seq(L4(n), n=1..60)];

MATHEMATICA

a[ n_] := Length @ FindInstance[{x1 > 0, x2 > 0, x3 > 0, x4 > 0, x5 > 0, n == x1 x2 + x2 x3 + x3 x4 + x4 x5}, {x1, x2, x3, x4, x5}, Integers, 10^9]; (* Michael Somos, Nov 12 2016 *)

CROSSREFS

Cf. A189835.

Sequence in context: A174658 A326300 A266074 * A238549 A237502 A279726

Adjacent sequences:  A191819 A191820 A191821 * A191823 A191824 A191825

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 17 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 12:44 EST 2019. Contains 329116 sequences. (Running on oeis4.)